## Trying to master Commutative property of addition

### Definition: (a + b) + c  =  a + (b + c)

The word “commutative” comes from “commute” or “move around”, so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is “a + b = b + a”; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is “ab = ba”; in numbers, this means 2×3 = 3×2.

### Easy to Remember Trick

Why “commutative” … ?

Because the numbers can travel back and forth like a commuter.

The word “commutative” comes from “commute” or “move around”, so the Commutative Property is the one that refers to moving stuff around. For addition, the rule is “a + b = b + a“; in numbers, this means 2 + 3 = 3 + 2. For multiplication, the rule is “ab = ba“; in numbers, this means 2×3 = 3×2. Any time they refer to the Commutative Property, they want you to move stuff around; any time a computation depends on moving stuff around, they want you to say that the computation uses the Commutative Property.

• #### Use the Commutative Property to restate “3×4×x” in at least two ways.

They want me to move stuff around, not simplify. In other words, my answer should not be “12x“; the answer instead can be any two of the following:

4 × 3 × x

4 × x × 3

3 × x × 4

x × 3 × 4

x × 4 × 3